holt mcdougal algebra 2 1-5 properties of exponents 1-5 properties of exponents warm up warm up...

Holt McDougal Algebra 2

1-5 Properties of Exponents1-5 Properties of Exponents

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Lesson QuizLesson Quiz



1-5 Properties of Exponents

Warm UpSimplify.

1. 4 4 4 2.

3. 4.

5. 6. 105

7. 3 104

64

20

100,000

30,000



Simplify expressions involving exponents.Use scientific notation.

Objectives



In an expression of the form an, a is the base, n is the exponent, and the quantity an is called a power. The exponent indicates the number of times that the base is used as a factor.



When the base includes more than one symbol, it is written in parentheses.

A power includes a base and an exponent. The expression 23 is a power of 2. It is read “2 to the third power” or “2 cubed.”

Reading Math



Write the expression in expanded form.

Example 1A: Writing Exponential Expressions in Expanded Form

The base is 5z, and the exponent is 2.

5z is a factor 2 times.

(5z)2

(5z)2

(5z)(5z)




Example 1B: Writing Exponential Expressions in Expanded Form

The base is s, and the exponent is 4.

s is a factor 4 times.

–s4

–s4

–(s s s s) = –s s s s




There are two bases: h and k + 3.

h is a factor 3 times, and k + 3 is a factor 2 times.

Example 1C: Writing Exponential Expressions in Expanded Form

3h3(k + 3)2

3h3(k + 3)2

3(h)(h)(h) (k + 3)(k + 3)



Check It Out! Example 1a


The base is 2a, and the exponent is 5.

2a is a factor 5 times.

(2a)5

(2a)5

(2a)(2a)(2a)(2a)(2a)



Check It Out! Example 1b


The base is b, and the exponent is 4.

b is a factor 4 times.

3b4

3 b b b b

3b4



Check It Out! Example 1c


There are two bases: 2x–1, and y.

2x–1 is a factor 3 times, and y is a factor 2 times.

–(2x – 1)3y2

–(2x – 1)3y2

–(2x – 1)(2x – 1)(2x – 1) y y



Caution!

Do not confuse a negative exponent with a negative expression.



Simplify the expression.

Example 2A: Simplifying Expressions with Negative Exponents

The reciprocal of .

3–2




Example 2B: Simplifying Expressions with Negative Exponents

The reciprocal of .





The reciprocal of .32

3 3 = 9





The reciprocal of .

(–5)–5

1 1 1 1 1 1

5 5 5 5 5 3125

51

5



Simplify the expression. Assume all variables are nonzero.

Example 3A: Using Properties of Exponents to Simplify Expressions

Product of Powers

Simplify.

3z7(–4z2)

3 (–4) z7 z2

–12z7 + 2

–12z9




Example 3B: Using Properties of Exponents to Simplify Expressions

Quotient of Powers

Negative of Exponent Property

Power of a Product

Power of a Product

(yz3 – 5)3 = (yz–2)3

y3(z–2)3

y3z(–2)(3)





Power of a Power

Power of a Product

(5x6)3

53(x6)3

125x(6)(3)

125x18



Negative Exponent Property

Power of a Power



(–2a3b)–3



Scientific notation is a method of writing numbers by using powers of 10. In scientific notation, a number takes a form m 10n, where1 ≤ m <10 and n is an integer.

You can use the properties of exponents to calculate with numbers expressed in scientific notation.



Simplify the expression. Write the answer in scientific notation.

Example 4A: Simplifying Expressions Involving Scientific Notation

Divide 4.5 by 1.5 and subtract exponents: –5 – 6 = –11.

3.0 10–11



Because 22.1 > 10, move the decimal point left 1 place and add 1 to the exponent.

Multiply 2.6 and 8.5 and add exponents: 4 + 7 = 11.


Example 4B: Simplifying Expressions Involving Scientific Notation

22.1 1011

(2.6)(8.5) (104)(107)

(2.6 104)(8.5 107)

2.21 1012



Check It Out! Example 4aSimplify the expression. Write the answer in scientific notation.

Because 0.25 < 10, move the decimal point right 1 place and subtract 1 from the exponent.

Divide 2.325 by 9.3 and subtract exponents: 6 – 9 = –3.

0.25 10–3

2.5 10–4



Because 12.4 >10, move the decimal point left 1 place and add 1 to the exponent.

Multiply 4 by 3.1 and add exponents: –6 – 4 = –10.



12.4 10–10

(4)(3.1) (10–6)(10–4)

(4 10–6)(3.1 10–4)

1.24 10–9



Lesson Quiz: Part I

Simplify each expression.

1. 4–3 2.

3. 8y6(–6y3)

Simplify each expression. Assume all

variables are nonzero.

4.

Simplify each expression. Write the answer in scientific notation.

5. 4.0 10–10

–48y9

holt mcdougal algebra 2 1-5 properties of exponents 1-5 properties of exponents warm up warm up...

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